Norman Calhoun brought this action under 42 U.S.C. § 1983 against Kenneth Ramsey, the Sheriff of Kane County, and Correctional Medical Services, Inc. (CMS), a private company that contracted with the County to provide medical care to inmates incarcerated in the county jail, complaining about injuries he sustained at the jail. He claimed that his injuries resulted from the fact that the jail’s medical policy made no provision for advance verification of a detainee’s medications. This omission, he argued, amounted to deliberate indifference to his medical needs in violation of the Eighth Amendment.
A jury found in favor of the defendants, and Calhoun now appeals. He complains about both the jury instructions on municipal liability and the introduction of certain evidence. We see no error with respect to either of these points, and we therefore affirm.
I
In 1999, Calhoun was sentenced to serve evenings and weekends at the Kane County Jail to satisfy a 120-day sentence for a motor vehicle violation. His sentence was to begin at 7:30 p.m. on June 1, 1999. In the days leading up to that time, Calhoun called the jail twice, in an effort to obtain pre-incarceration approval of his medication. He was doing so because he knew that detainees were not free simply to retain their own medications and take them as directed. Instead, consistent with the Illinois County Jail Standards, 20 Ill. Admin. Code § 701.40(j), the Kane County Jail’s medical policy requires that medication prescribed to inmates prior to incarceration must be verified and approved by the jail’s medical director before it can be administered to the inmate. CMS Policy 30.05. Moreover, “[a]ny medication in the possession of a detainee at admission shall be withheld until verification of its proper use is obtained and documented. This verification shall be made as soon as possible, but within the time interval specified for administration of the medication on the prescription container.” 20 Ill. Admin. Code § 701.40(j). Calhoun was hoping to complete these administrative steps before he actually reported to the jail.
Each time, his efforts were rebuffed. The jail personnel told him that pre-ap-proval was not important, and that he should just make arrangements at the time he checked in. On the evening of June 1, therefore, Calhoun arrived at the jail thirty minutes before the designated time. He reported to the booking area of the jail, where Officer Peter O’Connor took his intake information. Calhoun handed Officer O’Connor a bag containing eight prescription medications that he was taking and told the officer that he had to take some of the medication that night. The prescription labels on the bottles for two of the medications, Diazepam and Trazodone, stated that they had to be administered at “QHS,” a medical term referring to “hour of sleep.” The other medication did not have to be taken until the next morning. O’Connor placed Calhoun in a holding cell within the booking area. About fifteen minutes after his arrival at the jail, Lynn Kimmel, a nurse employed by CMS assigned to the jail, came to speak with him about his medications. As required by the jail’s policy, Kimmel took Calhoun’s prescription medicines with her when she left *378his cell, so that she could obtain authorization to administer them.
At around 8:30 p.m, Kimmel paged the jail physician and psychiatrist to obtain authorization to administer Calhoun’s medications. Half an hour later, the psychiatrist authorized Trazodone, to -be administered at “QHS,” which at the jail meant between 10 p.m. and 10:30 p.m. At around 9:15 p.m., jail officials notified Kimmel that Calhoun needed medical attention. She promptly returned to his cell, arriving around 9:20 p.m., where she found him lying on the floor complaining of pain. Kimmel was not authorized to administer medication without a doctor’s order, but she checked Calhoun’s vital signs, which showed elevated blood pressure. She then directed the jail staff to call for an ambulance. The, ambulance arrived at 9:45 p.m. and transported Calhoun to the hospital, where he was treated in the emergency room. The hospital discharged Calhoun in good condition at 11:30 p.m., a little more than one hour after his arrival at the hospital and four hours after his report time. He did not return to the jail that night or subsequently because he was released from the Sheriffs custody at that time and was not required to serve the rest of his sentence at the jail.
Believing that the events of June 1 demonstrated deliberate indifference to his medical needs in violation of the Eighth Amendment, Calhoun filed suit against Sheriff Ramsey, CMS, Officer O’Connor and Nurse Kimmel under 42 U.S.C. § 1983. Calhoun alleged that he had been injured as a result of the jail’s failure to administer his medication in a timely fashion. The jail’s failure, he asserted, was the result of a constitutionally inadequate policy: specifically, a policy that made no provision - for advance verification of medication and indeed prohibited this approach, as illustrated by the refusal of the jail personnel to respond positively to Calhoun’s efforts to obtain approval for his medications before he reported to serve his sentence. The district court granted summary judgment in favor of defendants O’Connor and Kimmel and partial summary judgment in favor of CMS and Ramsey on some claims. Calhoun does not appeal from these rulings.
The only claim presented to the jury was the one against the Sheriff and CMS in which Calhoun alleged that the absence of a pre-verification procedure in the jail’s policy and the jail’s refusal to verify his medication in advance amounted to deliberate indifference to his medical needs. After a trial, the jury found in favor of CMS and Ramsey.
Calhoun appeals the jury verdict on two grounds. First, he alleges that the jury instructions misstated the law by requiring “evidence that the circumstances he endured were not an isolated incident,” but had been caused by a “widespread policy or practice that was so permanent and well settled as to constitute a custom or usage with the force of law.” Second, he argues that the court improperly permitted the defendants to introduce extrinsic evidence to impeach him on a collateral matter.
II
Calhoun objects that the jury instructions misstated the law on municipal liability, at least for a claim like his that postulated liability under § 1983 through an express policy. He argues that evidence of only one violation is sufficient for finding liability under this theory. On that assumption, he continues, the following portions of the jury instructions were erroneous:
In order to prove that the defendants had a deliberately indifferent policy or practice, the plaintiff must establish that there existed a wide-spread policy or *379practice that was so permanent and well-settled as to constitute a custom or usage with the force of law.
For purposes of proving a widespread practice that is so permanent and well-settled as to constitute a custom or usage with the force of law, the plaintiff is required to present evidence that the circumstances that he endured was not an isolated incident. (Emphasis added.)
We review jury instructions de novo to determine whether they provide fair and accurate summaries of the law. United States v. Tingle, 183 F.3d 719, 729 (7th Cir.1999). We give the district court substantial discretion with respect to the precise wording of jury instructions so long as the final result, read as a whole, completely and correctly states the law. See id. Even if the instruction contains an error or misguides the jury, we reverse a jury verdict only if the error prejudiced a litigant. See Molnar v. Booth, 229 F.3d 593, 602 (7th Cir.2000).
We must first address the defendants’ assertion that Calhoun waived this argument by objecting at trial only to the first paragraph reproduced above but not to the second. It is true that a litigant’s failure to raise an objection before the trial court that would alert the court to the basis of a perceived defect precludes appellate review. See Haley v. Gross, 86 F.3d 630, 644 (7th Cir.1996). As the first instruction requires a showing of more than one incident, however, we think that Calhoun sufficiently alerted the court to the argument he now advances, namely, that he is not required to present evidence of other incidents of violations resulting from a municipality’s express policy under § 1983. Therefore, we can reach the merits of this claim.
In Monell v. N.Y. City Dept. of Social Servs., 436 U.S. 658, 98 S.Ct. 2018, 56 L.Ed.2d 611 (1978), the Supreme Court established both the fact that “municipalities and other local government units [were] included among those persons to whom § 1983 applies,” id. at 690, 98 S.Ct. 2018, and the limits of such actions. Most importantly, Monell held that “a municipality cannot be held liable under § 1983 on a respondeat superior theory.” Id. at 691, 98 S.Ct. 2018. Instead, municipal liability exists only “when execution of a government’s policy or custom, whether made by its lawmakers or by those whose edicts or acts may fairly be said to represent official policy, inflicts the injury.” Id. at 694, 98 S.Ct. 2018. We have identified three different ways in which a municipality or other local governmental unit might violate § 1983:(1) through an express policy that, when enforced, causes a constitutional deprivation; (2) through a “widespread practice” that although not authorized by written law and express policy, is so permanent and well-settled as to constitute a “custom or usage” with the force of law; or (3) through an allegation that the constitutional injury was caused by a person with “final decision policymaking authority.” McTigue v. City of Chi, 60 F.3d 381, 382 (7th Cir.1995).
The express policy theory applies, as the name suggests, where a policy explicitly violates a constitutional right when enforced. See Monell, 436 U.S. at 658, 98 S.Ct. 2018. So, for example, if the Kane County Jail had a policy that directed the sheriffs personnel to throw away all prescription medications brought in by detainees or prisoners without even reading the label and without making alternative provisions for the affected individuals, the County would be liable assuming that such a policy would, on its face, violate the Eighth Amendment (or the Due Process clause, for pre-trial detainees). Under this type of claim, one application of the offen*380sive policy resulting in a constitutional violation is sufficient to establish municipal liability. City of Okla. v. Tuttle, 471 U.S. 808, 822, 105 S.Ct. 2427, 85 L.Ed.2d 791 (1985).
A second way of complaining about an express policy is to object to omissions in the policy. This, as we understand the argument, is what Calhoun is doing. In fact, we think that it is more confusing than useful to distinguish between claims about express policies that fail to address certain issues, and claims about widespread practices that are not tethered to a particular written policy. In both of these situations, the claim requires more evidence than a single incident to establish liability. See Tuttle, 471 U.S. at 822-23, 105 S.Ct. 2427 (challenging the city’s police officer training policy as inadequate). This is because it is necessary to understand what the omission means. No government has, or could have, policies about virtually everything that might happen. The absence of a policy might thus mean only that the government sees no need to address the point at all, or that it believes that case-by-case decisions are best, or that it wants to accumulate some experience before selecting a regular course of action. At times, the absence of a .policy might reflect a decision to act unconstitutionally, but the Supreme Court has repeatedly told us to be cautious about drawing that inference. See, e.g., Bd. of the County Comm’rs of Bryan County v. Brown, 520 U.S. 397, 409, 117 S.Ct. 1382, 137 L.Ed.2d 626 (1997) (rejecting Monell claim based on absence of more thorough screening of candidates for sheriffs deputy); City of Canton v. Harris, 489 U.S. 378, 388, 109 S.Ct. 1197, 103 L.Ed.2d 412 (1989) (rejecting a failure-to-train claim).
Both in the “widespread practice” implicit policy cases and in the cases attacking gaps in express policies, what is needed is evidence that there is a true municipal policy at issue, not a random event. If the same problem has arisen many times and the municipality has acquiesced in the outcome, it is possible (though not necessary) to infer that there is a policy at work, not the kind of isolated incident that Brown held cannot support municipal liability. So, for example, in addressing whether a city’s failure adequately to train its police officers amounted to a policy for Monell purposes, the Supreme Court had the following to say:
[T]he word “policy” generally implies a course of action consciously chosen from among various alternatives; it is therefore difficult in one sense even to accept the submission that someone pursues a “policy” of “inadequate training,” unless evidence be adduced which proves that the inadequacies resulted from conscious choice — that is, proof that the policymakers deliberately chose a training program which would prove inadequate.
Tuttle, 471 U.S. at 823, 105 S.Ct. 2427 (footnote omitted); see also Harris, 489 U.S. at 388, 109 S.Ct. 1197 (finding liability should be imposed only when the degree of fault rises to the level of “deliberate indifference” to rights, that is, where the municipality’s “choice to follow a course of action is made from among various alternatives by '... policymakers.”) (quoting Pembaur v. Cincinnati, 475 U.S. 469, 483-84, 106 S.Ct. 1292, 89 L.Ed.2d 452 (1986) (Brennan, J., plurality)).
Accordingly, the Court has held that “where the policy relied upon is not itself unconstitutional, considerably more proof than the single incident will be necessary in every case to establish both the requisite fault on the part of the municipality and the causal connection between the [omission in the policy] and the constitutional deprivation.” Tuttle, 471 U.S. at *381824, 105 S.Ct. 2427 (footnote omitted). Even though the Court in Harris did not absolutely foreclose the possibility that a plaintiff might succeed in proving a failure-to-train claim without showing a pattern of constitutional violations, see 489 U.S. at 390 & n. 10, 109 S.Ct. 1197, it later clarified that it was “simply hypothesizing] that, in a narrow range of circumstances, a violation of federal rights may be a highly predictable consequence of a failure to equip law enforcement officers with specific tools to handle recurring situations.” Brown, 520 U.S. at 409, 117 S.Ct. 1382. Although the Court has therefore left room for this “narrow range of circumstances,” it is telling that no court has directly addressed such a case. Cf. Woodward v. Correctional Medical Services, 368 F.3d 917, 929 (7th Cir.2004) (commenting that evidence of .a single violation may be enough where a jail takes no precautions against the possibility of inmate suicide but imposing liability based on the jail’s repeated failures to ensure one inmate’s safety and condoning violations of its own suicide-watch policy).
Against this backdrop, we have no trouble concluding that there was nothing wrong with the jury instructions to which Calhoun has objected. Whether we look at this case as one in which Calhoun was complaining about the failure of the County’s express policy to make provision for advance verification of medications, or if we look at it as one in which Calhoun is arguing that the County has an implicit policy reflected in an alleged widespread practice of impeding detainee access to medication (a distinction Calhoun has discussed at length), the result is the same. Because he cannot point to any language in the jail’s policy that is constitutionally suspect, he must provide enough evidence of custom and practice to permit an inference that the County has chosen an impermissible way of operating. Calhoun did not even try to show that Kane County’s affirmative decision to require that medication must be verified “within the time interval specified for administration of the medication on the prescription container,” see 20 Ill. Admin. Code § 701.40(j), was so inadequate as to amount to an Eighth Amendment violation. This strategic decision was a wise one. First, the County’s policy uses a time interval between doses that even the prescribing physician apparently believes is appropriate for the particular patient. Second, this court has upheld another jail’s policy, identical to the one in Kane County, which is also based on the Illinois County Jail Standards, 20 Ill. Admin. Code § 701.40(j). See Garvin v. Armstrong, 236 F.3d 896 (7th Cir.2001).
Having argued that the jail had a “practice of refusing” to pre-verify medication, Calhoun cannot now turn around and argue that the district court erred by instructing the jury on a custom or usage theory. Indeed, the instructions were consistent with Calhoun’s proposed instructions and provided an alternative theory for his claim. His effort to hold Kane County liable on the basis of this single incident is inconsistent with Brown, and the district court was correct to reject instructions that would have misstated the law.
Ill
Calhoun’s other argument on appeal relates to a decision by the district court to admit certain impeachment evidence. At trial, Calhoun testified that he had been working in June 1999 when he reported to the jail to begin his work-release sentence. On cross-examination, the defendants confronted him with sworn statements he had made to the Social Security Administration in an application for disability benefits. In the application, Calhoun stated that he had *382become unable to work in November 1998. Calhoun now argues that these statements related to a collateral matter and were therefore inadmissible.
We have held that “a witness may not be impeached by contradiction as to collateral or irrelevant matters elicited on cross-examination. A matter is collateral if the impeaching fact could not have been introduced into evidence for any purpose other than the contradiction.” Taylor v. Nat’l R.R. Passenger Corp., 920 F.2d 1372, 1375 (7th Cir.1990) (internal citation and quotation marks omitted). In other words, a party may not “contradict for the sake of contradiction.” United States v. Bitterman, 320 F.3d 723, 727 (7th Cir.2003) (quotation marks omitted).
In permitting the defendants to introduce the statements in Calhoun’s disability application, the court held that they were not about a collateral matter because they related to one of the essential issues -of the case: Calhoun’s physical condition both before and after the events at the jail. The court noted that this issue was material to the question of damages and that it was Calhoun’s contention that his condition after June 1, 1999, was much worse than it had been before. The statements in the application reveal that Calhoun was unable to work prior to the jail incident. Thus, whatever their effect may have been on his credibility, those statements were relevant to the question of the extent, if any, of the effect the incident had on his overall condition.
We agree with the district court that Calhoun’s statements to the Social Security Administration did not relate to a collateral matter. They threw light on a material issue in the case — his condition before the events at the jail — and therefore they were admissible. The district did not abuse its discretion in admitting this evidence.
IV
For these reasons, we AffiRM the judgment.